A numerical algorithm for computation modelling of 3D nonlinear wave equations based on exponential modified cubic B-spline differential quadrature method

ABSTRACT

In this paper, the authors proposed a method based on exponential modified cubic B-spline differential quadrature method (Expo-MCB-DQM) for the numerical simulation of three dimensional (3D) nonlinear wave equations subject to appropriate initial and boundary conditions. This work extends the idea of Tamsir et al. [An algorithm based on exponential modified cubic B-spline differential quadrature method for nonlinear Burgers’ equation, Appl. Math. Comput. 290 (2016), pp. 111–124] for 3D nonlinear wave type problems. Expo-MCB-DQM transforms the 3D nonlinear wave equation into a system of ordinary differential equations (ODEs). To solve the resulting system of ODEs, an optimal five stage and fourth-order strong stability preserving Runge–Kutta (SSP-RK54) scheme is used. Stability analysis of the proposed method is also discussed and found that the method is conditionally stable. Four test problems are considered in order to demonstrate the accuracy and efficiency of the algorithm.

KEYWORDS:

• Three dimensional nonlinear wave equations
• Expo-MCB-DQM
• SSP-RK54

2000 AMS SUBJECT CLASSIFICATIONS:

• 65D07
• 65N30
• 65N35
• 74S05

Acknowledgements

The authors are very thankful to the editor and reviewers for their valuable suggestions to improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.